Undergraduate Course: Classical Mechanics for Mathematicians (MATH10106)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 10 (Year 3 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  Classical mechanics deals with the mathematical description of the motion of bodies, or pointlike objects. By understanding the forces that are exerted on a body we can construct Newton's equation that describes the motion of the object in question. There are however, other mathematical approaches to this class of problems, known as the Lagrangian and Hamiltonian descriptions of classical mechanics. This course will introduce these various perspectives, and in the process cover the subject of the calculus of variations. Furthermore this course is the first in a series of mathematical physics courses, such as Quantum Mechanics, Classical Field theory, Quantum Information, Geometry of General Relativity and Topics in Mathematical Physics A/B. 
Course description 
This course is an introduction to the subject of classical mechanics. It will cover Newton's equation, the motion of point particles, including planetary motion, and an introduction to the notion of variational calculus for point particles. In particular the course will cover Hamilton's principle of least action, Lagrangians for systems with conservative forces, and Noether's theorem. The latter provides a conserved quantity whenever there exists a continuous symmetry. Finally, an introduction to the Hamiltonian formalism will be given which prepares the ground for the followup course on quantum mechanics for mathematicians. The classical mechanics for mathematicians course is a great opportunity to learn about many classical differential equations and physical problems that helped shape many developments in mathematics. It is also a nice arena to practise one's knowledge of several variable calculus and differential equations.
The course will include the following topics:
 Newton's equations for simple mechanical systems
 Celestial mechanics
 Lagrangians and EulerLagrange equations
 Noether's theorem and continuous symmetries
 Hamiltonians and Hamilton's equations
 Poisson brackets

Information for Visiting Students
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2024/25, Available to all students (SV1)

Quota: None 
Course Start 
Semester 2 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 18,
Supervised Practical/Workshop/Studio Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
73 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework: 20%, Examination 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)   2:00  
Learning Outcomes
On completion of this course, the student will be able to:
 Solve Newton's equation for simple mechanical systems
 Construct Lagrangians for simple mechanical systems
 Compute conserved charges using Noether's theorem
 Construct Hamiltonians starting from a Lagrangian
 Compute with Poisson brackets

Reading List
The course will be based on lecture notes. Recommended in addition to materials provided:
 (*) Herbert Goldstein, Classical Mechanics
 (*) Landau and Lifshitz, Mechanics, Course of Theoretical Physics, Volume 1
 (*) Marion and Thornton, Classical Dynamics (of particles and systems)
¿ Arnold, Mathematical Methods of Classical Mechanics (chapters 1 to 3)
(*) are available to download from the University Library 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  CMech,Classical Mechanics,Lagrangians,Hamiltonians,Noether¿s theorem 
Contacts
Course organiser  Dr Timothy Adamo
Tel:
Email: t.adamo@ed.ac.uk 
Course secretary  Miss Greta Mazelyte
Tel:
Email: greta.mazelyte@ed.ac.uk 

